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$ L(X,C(K))$ as a dual space


Author: T. S. S. R. K. Rao
Journal: Proc. Amer. Math. Soc. 110 (1990), 727-729
MSC: Primary 47D15; Secondary 46A32, 46B10
DOI: https://doi.org/10.1090/S0002-9939-1990-1023355-X
MathSciNet review: 1023355
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Abstract: We exhibit a class of Banach spaces $ X$, with $ {X^*}$ having nontrivial centralizer for which the space of operators $ L(X,C(K))$ is a dual space implies that $ K$ is hyperstonian.


References [Enhancements On Off] (What's this?)

  • [1] E. Behrends, $ M$-structure and the Banach-Stone theorem, Lecture Notes in Math. vol. 736, Springer-Verlag, 1979. MR 547509 (81b:46002)
  • [2] -, On the geometry of spaces of $ {C_0}K$-valued operators, Studia. Math. 90 (1988), 135-151. MR 954168 (89k:46006)
  • [3] M. Cambern and P. Greim, Uniqueness of preduals for spaces of continuous vector functions, Canad. Math. Bull. 32 (1989), 98-104. MR 996129 (90g:46057)
  • [4] J. Diestel and J. J. Uhl, Vector measures, Amer. Math. Soc. Surveys, vol. 15, Providence, Rl. MR 0453964 (56:12216)
  • [5] H. E. Lacey, The isometric theory of classical Banach spaces, Springer-Verlag, Band 208, 1974. MR 0493279 (58:12308)
  • [6] D. Li, Espaces $ L$-facteurs de leurs biduaux: Bonne disposition, Meilleure approximation et propriete de Radon-Nikodym, Quart J. Math. 38 (1987), 229-243. MR 891618 (88h:46024)
  • [7] A. Lima, Intersection properties of balls in spaces of compact operators, Ann. Inst. Fourier, Grenoble 28 (1978), 35-65. MR 511813 (80g:47048)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1990-1023355-X
Keywords: Space of operators, $ M$-structure, centralizer, hyperstonian spaces
Article copyright: © Copyright 1990 American Mathematical Society

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